Advertisement

Adaptive fractional order fast terminal dynamic sliding mode controller design for antilock braking system (ABS)

  • Seyyed Sajjad MoosapourEmail author
  • Sayed Bagher Fazeli Asl
  • Morteza Azizi
Article
  • 109 Downloads

Abstract

This article focuses on designing an antilock braking system (ABS) controller to adjust the wheel slip to the preferred value using sliding mode control and fractional calculus. The ABS must be robust against external disturbances such as variations in the friction force between the tire and road caused by changes in the road conditions, loadings and etc. A fractional order PD switching surface is defined, then in order to improve the convergence speed and increase degree of freedom of the controller, a new sliding surface is defined as fast terminal dynamic sliding surface which is formulated using Fractional Calculus. Then, a fractional order fast terminal dynamic sliding mode controller (FOFTDSMC) is designed. Also, for estimating the upper bound value of the lumped uncertainty in the proposed controller, an adaptive FOFTDSMC is designed. The finite time stability of the closed-loop system is guaranteed. Simulation results show the effectiveness of the proposed controller in terms of fast tracking with high robustness when compared to the fractional order sliding mode controller and fractional order fast terminal sliding mode controller.

Keywords

Robust Uncertainty Finite time Lyapunov Stability 

References

  1. 1.
    Sae Standard (1992) Anti-lock brake system review. SAE J 2246Google Scholar
  2. 2.
    Kost F, Ehret T, Wagner J, Papert U, Heinen F et al (2015) Antilock braking system (ABS). In: Reif K (ed) Automotive mechatronics. Springer, Wiesbaden, pp 354–369Google Scholar
  3. 3.
    John S, Pedro JO (2013) Hybrid feedback linearization slip control for anti-lock braking system. Acta Polytech Hung 10(1):81–99Google Scholar
  4. 4.
    Aksjonov A, Augsburg K, Vodovozov V (2016) Design and simulation of the robust ABS and ESP fuzzy logic controller on the complex braking maneuvers. Appl Sci 6(12):382CrossRefGoogle Scholar
  5. 5.
    Lin CM, Hsu CF (2003) Neural-network hybrid control for antilock braking systems. IEEE Trans Neural Netw 14(2):351–359MathSciNetCrossRefGoogle Scholar
  6. 6.
    John S, Pedro JO (2013) Neural network-based adaptive feedback linearization control of antilock braking system. Int J Artif Intell 10(S13):21–40Google Scholar
  7. 7.
    Zhang C, Ordonez R (2007) Numerical optimization-based extremum seeking control with application to ABS design. IEEE Trans Autom Control 52(3):454–467MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Tang Y, Wang Y, Han M, Lian Q (2016) Adaptive fuzzy fractional-order sliding mode controller design for antilock braking systems. J Dyn Syst Meas Control 138(4):041008CrossRefGoogle Scholar
  9. 9.
    Perić SL, Antić DS, Milovanović MB, Mitić DB, Milojković MT, Nikolić SS (2016) Quasi-sliding mode control with orthogonal endocrine neural network-based estimator applied in anti-lock braking system. IEEE/ASME Trans Mechatron 21(2):754–764CrossRefGoogle Scholar
  10. 10.
    Harifi A, Aghagolzadeh A, Alizadeh G, Sadeghi M (2008) Designing a sliding mode controller for slip control of antilock brake systems. Transp Res Part C Emerg Technol 16(6):731–741CrossRefGoogle Scholar
  11. 11.
    Okyay A, Cigeroglu E, Başlamışlı SÇ (2013) A new sliding-mode controller design methodology with derivative switching function for anti-lock brake system. Proc Inst Mech Eng Part C J Mech Eng Sci 227(11):2487–2503CrossRefGoogle Scholar
  12. 12.
    Li L, Zhang Y, Yang C, Yan B, Martinez CM (2016) Model predictive control-based efficient energy recovery control strategy for regenerative braking system of hybrid electric bus. Energy Convers Manag 111:299–314CrossRefGoogle Scholar
  13. 13.
    Yu H, Taheri S, Duan J, Qi Z (2016) An integrated cooperative antilock braking control of regenerative and mechanical system for a hybrid electric vehicle based on intelligent tire. Asian J Control 18(1):55–68MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Topalov AV, Oniz Y, Kayacan E, Kaynak O (2011) Neuro-fuzzy control of antilock braking system using sliding mode incremental learning algorithm. Neurocomputing 74(11):1883–1893CrossRefGoogle Scholar
  15. 15.
    Unsal C, Kachroo P (1999) Sliding mode measurement feedback control for antilock braking systems. IEEE Trans Control Syst Technol 7(2):271–281CrossRefGoogle Scholar
  16. 16.
    Lian H, Chong KT (2006) Variable parameter sliding controller design for vehicle brake with wheel slip. J Mech Sci Technol 20(11):1801–1812CrossRefGoogle Scholar
  17. 17.
    Kayacan E, Oniz Y, Kaynak O (2009) A grey system modeling approach for sliding-mode control of antilock braking system. IEEE Trans Ind Electron 56(8):3244–3252CrossRefGoogle Scholar
  18. 18.
    Petras I (2011) Fractional-order nonlinear systems: modeling, analysis and simulation. Springer, BerlinCrossRefzbMATHGoogle Scholar
  19. 19.
    Podlubny I (1998) Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Academic Press, Cambridge, p 198Google Scholar
  20. 20.
    Azar AT, Vaidyanathan S, Ouannas A, editors (2017) Fractional order control and synchronization of chaotic systems. 688, SpringerGoogle Scholar
  21. 21.
    Couceiro MS, Ferreira NF, Machado JT (2010) Application of fractional algorithms in the control of a robotic bird. Commun Nonlinear Sci Numer Simul 15(4):895–910CrossRefGoogle Scholar
  22. 22.
    Aguila-Camacho N, Duarte-Mermoud MA, Gallegos JA (2014) Lyapunov functions for fractional order systems. Commun Nonlinear Sci Numer Simul 19(9):2951–2957MathSciNetCrossRefGoogle Scholar
  23. 23.
    Zou Q, Jin Q, Zhang R (2016) Design of fractional order predictive functional control for fractional industrial processes. Chemometr Intell Lab Syst 152:34–41CrossRefGoogle Scholar
  24. 24.
    Oustaloup A, Moreau X, Nouillant M (1996) The CRONE suspension. Control Eng Pract 4(8):1101–1108CrossRefGoogle Scholar
  25. 25.
    Vinagre BM, Podlubny I, Dorcak L, Feliu V (2000) On fractional PID controllers: a frequency domain approach. In: Proceedings of IFAC workshop on digital control-PID, Terrassa, SpainGoogle Scholar
  26. 26.
    Valerio D, Sada Cost J (2013) Variable order fractional controllers. Asian J Control 15(3):648–657MathSciNetCrossRefGoogle Scholar
  27. 27.
    Padula F, Visioli A (2013) Set-point weight tuning rules for fractional-order PID controllers. Asian J Control 15(3):678–690MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Domek S (2013) Switched state model predictive control of fractional-order nonlinear discrete-time systems. Asian J Control 15(3):658–668MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Fsyszi A, Rafsanjani HN (2011) Fractional order fuzzy sliding mode controller for robotic flexible joint manipulators. In: 9th IEEE international conference on control and automation (ICCA)Google Scholar
  30. 30.
    Tang Y, Zhang X, Zhang D, Zhao G, Guan X (2013) Fractional order sliding mode controller design for antilock braking systems. Neurocomputing 111:122–130CrossRefGoogle Scholar
  31. 31.
    Delavari H, Ranjbar AN, Ghaderi R, Momani S (2010) Fractional order control of a coupled tank. Nonlinear Dyn 61(3):383–397MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Sutha S, Lakshmi P, Sankaranarayanan S (2015) Fractional-order sliding mode controller design for a modified quadruple tank process via multi-level switching. Comput Electr Eng 45:10–21CrossRefGoogle Scholar
  33. 33.
    Ullah N, Shaoping W, Khattak MI, Shafi M (2015) Fractional order adaptive fuzzy sliding mode controller for a position servo system subjected to aerodynamic loading and nonlinearities. Aerosp Sci Technol 43:381–387CrossRefGoogle Scholar
  34. 34.
    Venkataraman S, Gulati S (1993) Control of nonlinear systems using terminal sliding modes. J Dyn Syst Meas Control 115(3):554–560CrossRefzbMATHGoogle Scholar
  35. 35.
    Xu JX, Guo ZQ, Lee TH (2014) Design and implementation of integral sliding-mode control on an underactuated two-wheeled mobile robot. IEEE Trans Ind Electron 61(7):3671–3681CrossRefGoogle Scholar
  36. 36.
    Lee J, Chang PH, Jin M (2017) Adaptive integral sliding mode control with time-delay estimation for robot manipulators. IEEE Trans Ind Electron 64(8):6796–6804CrossRefGoogle Scholar
  37. 37.
    Li S, Zhou M, Yu X (2013) Design and implementation of terminal sliding mode control method for PMSM speed regulation system. IEEE Trans Ind Inf 9(4):1879–1891CrossRefGoogle Scholar
  38. 38.
    Khoo S, Yin J, Man Z, Yu X (2013) Finite-time stabilization of stochastic nonlinear systems in strict-feedback form. Automatica 49(5):1403–1410MathSciNetCrossRefzbMATHGoogle Scholar
  39. 39.
    Meng Z, Ren W, You Z (2010) Distributed finite-time attitude containment control for multiple rigid bodies. Automatica 46(12):2092–2099MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Chen M, Wu QX, Cui RX (2013) Terminal sliding mode tracking control for a class of SISO uncertain nonlinear systems. ISA Trans 52(2):198–206CrossRefGoogle Scholar
  41. 41.
    Dadras S, Momeni HR (2012) Fractional terminal sliding mode control design for a class of dynamical systems with uncertainty. Commun Nonlinear Sci Numer Simul 17(1):367–377MathSciNetCrossRefzbMATHGoogle Scholar
  42. 42.
    Chen SY, Gong SS (2017) Speed tracking control of pneumatic motor servo systems using observation-based adaptive dynamic sliding-mode control. Mech Syst Signal Process 94:111–128CrossRefGoogle Scholar
  43. 43.
    Tiwari J (2014) Dynamic sliding mode control of four dimensional hyperchaotic systems using LMI. In: International conference on advances in engineering and technology research (ICAETR), pp 1–4Google Scholar
  44. 44.
    Singh VK, Pillai G (2015) Dynamic sliding mode control of partially linear chaotic system. In: 39th National Systems Conference (NSC), pp 1–4Google Scholar
  45. 45.
    Cong B, Liu X, Chen Z (2013) Backstepping based adaptive sliding mode control for spacecraft attitude maneuvers. Aerosp Sci Technol 30(1):1–7CrossRefGoogle Scholar
  46. 46.
    Lu C, Fei J (2016) Adaptive sliding mode control of MEMS gyroscope with prescribed performance. In: 14th international workshop on variable structure systems (VSS), pp 65–70Google Scholar
  47. 47.
    Sharkawy AB (2010) Genetic fuzzy self-tuning PID controllers for antilock braking systems. Eng Appl Artif Intell 23(7):1041–1052CrossRefGoogle Scholar
  48. 48.
    Burckharda M (1993) Fahrwerktechnik: radschlupf-regelsysteme. Vogel-Verlag, München, pp 1–16Google Scholar
  49. 49.
    Ramadan HS (2017) Optimal fractional order PI control applicability for enhanced dynamic behavior of on-grid solar PV systems. Int J Hydrogen Energy 42(7):4017–4031CrossRefGoogle Scholar
  50. 50.
    Aghababa MP (2012) Comments on “Fuzzy fractional order sliding mode controller for nonlinear systems”[Commun Nonlinear Sci Numer Simulat 15 (2010) 963–978]. Commun Nonlinear Sci Numer Simul 17(3):1489–1492MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Seyyed Sajjad Moosapour
    • 1
    Email author
  • Sayed Bagher Fazeli Asl
    • 1
  • Morteza Azizi
    • 1
  1. 1.Department of Electrical Engineering, Faculty of EngineeringShahid Chamran University of AhvazAhvazIran

Personalised recommendations